fitL_explicit = glm(y~age, family=gaussian(link="identity"), data=d)

fitL = glm(y~age, data=d)
effL = data.frame(allEffects(fitL,xlevels=list(age=seq(min(age),max(age),.05)))$"age")
ggplot(d,aes(x=age,y=y))+
  coord_cartesian(ylim=c(-0.4,max(y))) +
  geom_point(size=4,alpha=.5,color="darkblue")+
  geom_line(data=effL,aes(y=fit),size=2,color="darkred")+
  geom_ribbon(data=effL,aes(y=fit,ymin=lower,ymax=upper),alpha=.3,fill="darkred")+
  theme(text=element_text(size=ts,color="black"))+
  scale_y_continuous(breaks=seq(0,20,2))+scale_x_continuous(breaks=seq(0,20,.5))+
  ylab("Errors")+xlab("Age (years)")

fitP = glm(y~age, family=poisson(link="log"), data=d)

effP = data.frame(allEffects(fitP,xlevels=list(age=seq(min(age),max(age),.05)))$"age")
ggplot(d,aes(x=age,y=y))+
  coord_cartesian(ylim=c(-0.4,max(y))) +
  geom_point(size=4,alpha=.5,color="darkblue")+
  geom_line(data=effP,aes(y=fit),size=2,color="blue")+
  geom_ribbon(data=effP,aes(y=fit,ymin=lower,ymax=upper),alpha=.3,fill="blue")+
  #geom_line(data=effL,aes(y=fit),size=2,color="darkred")+
  #geom_ribbon(data=effL,aes(y=fit,ymin=lower,ymax=upper),alpha=.3,fill="darkred")+
  theme(text=element_text(size=ts,color="black"))+
  scale_y_continuous(breaks=seq(0,20,2))+scale_x_continuous(breaks=seq(0,20,.5))+
  ylab("Errors")+xlab("Age (years)")

ts <- 16
tc <- "black"

eff_obj <- allEffects(
  fitL_1,
  xlevels = list(age = seq(min(d$age), max(d$age), .05))
)[["age:group"]]

effL <- as.data.frame(eff_obj)

# garantisci colonna fit
if (!("fit" %in% names(effL))) {
  pred_col <- intersect(c("fit", "response", "fitted", "yhat"), names(effL))
  if (length(pred_col) == 0)
    stop("Nessuna colonna di predizione trovata in effL.")
  effL$fit <- effL[[pred_col[1]]]
}

ggplot(d, aes(x = age, y = y, shape = group, color = group)) +
  geom_point(size = 4, alpha = .6) +
  geom_ribbon(
    data = effL,
    aes(x = age, ymin = lower, ymax = upper, fill = group, group = group),
    alpha = .3,
    color = NA,
    inherit.aes = FALSE
  ) +
  geom_line(
    data = effL,
    aes(x = age, y = fit, color = group, group = group),
    linewidth = 2,
    inherit.aes = FALSE
  ) +
  scale_color_manual(values = c("darkorange3", "darkgreen")) +
  scale_fill_manual(values = c("darkorange3", "darkgreen")) +
  theme(text = element_text(size = ts, color = tc)) +
  scale_x_continuous(breaks = seq(6, 10, .5)) +
  labs(y = "Errors", x = "Age (years)")

fitP = glm(y~age*group, family=poisson(link="log"), data=d)
effP = data.frame(allEffects(fitP,xlevels=list(age=seq(min(age),max(age),.05)))$"age:group")
effP$group = as.factor(effP$group)
ggplot(d,aes(x=age,y=y,shape=group,color=group))+
  geom_point(size=4,alpha=.6)+
  scale_color_manual(values=c("darkorange2","darkgreen"))+
  scale_fill_manual(values=c("darkorange1","darkgreen"))+
  geom_line(data=effP,aes(x=age,y=fit,group=group,linetype=group),size=2)+
  geom_ribbon(data=effP,aes(x=age,y=fit,ymin=lower,ymax=upper,group=group,fill=group),alpha=.3,color=NA)+
  theme(text=element_text(size=ts,color="black"))+scale_x_continuous(breaks=seq(0,20,.5))+
  ylab("Errors")+xlab("Age (years)")